The physical parameters being used most often in oil and gas exploration are velocities and densities of rocks and wave impedance calculated from them. These physical parameters are appropriate for determining underground structures. Nevertheless they result in uncertainty in determining rock property and for direct hydrocarbon detection. Two reasons account for such uncertainty: (1) the variation ranges of velocities and densities for variety of rocks overlap each other to some extent. (2) P-wave velocity, S-wave velocity and density are closely related each other. They have very limited ability for compensating each other to indicate the variation of characteristics of rocks and their pore-filling fluid.
Elastic moduli of rock include Lame constants .DELTA. and shear modulus .mu., the bulk modulus .kappa., Young's modulus E and Poisson's ration .sigma.. Their first introduction into physics was in the field of material science. The way by which they are defined makes them all positive. Those five elastic moduli are not independent from each other. Any one of them can be expressed in terms of two others. Therefore the elastic moduli played an important role in wave equation theory development. It is usually difficult to measure the moduli directly. They are usually calculated using the shear- and compressional-wave velocity and density measured in lab.
Shear-wave velocity V.sub.s and compressional-wave velocity V.sub.p are related to elastic moduli in terms of density .rho.. For example ##EQU1## By original meaning, rock's velocities in seismic exploration indicate only how fast the seismic waves travel through rock. Velocity has indirect relations to characteristics of rock and its pore-filling-fluid. Velocity results from comprehensive effect of moduli and density. Moduli, as compared with velocities, are more closely and more directly related to characteristics of rock and its pore-filling-fluid. The relative changes of elastic moduli and that of densities of geologic formations may have better ability to indicate changes in characteristics of geologic formations and their pore-filling-fluid directly. Therefore determining relative changes of elastic moduli and densities of geologic formations will be very useful for rock property study and direct hydrocarbon detection.
The Common-Depth-Point technique (hereinafter referred to as CDP technique) is one of the techniques which experienced great successes in the field of oil and gas exploration. The CDP technique have been developed and refined over forty years. Assuming a horizontally layered geologic formation, multiple coverage seismic data from each subsurface point can be recorded with CDP technique by using appropriate surface-detector and shot-point spreads. By sorting the seismic data recorded, CDP gathers can be composed. Stacking the traces within one CDP gather will enhance primary reflections from the same sub-surface reflection point and reduce multiple reflections and random noise. Unfortunately, while enhancing primary reflections, CDP stacking destroys valuable seismic information which is of crucial importance for direct hydrocarbon detection.
It has been recognized in theory since at least the end of last century that the amplitudes of shear and compressional reflectivity at a reflection boundary change with the angle of incidence. One of outstanding works is Zoeppritz equations which show that changing of the reflectivity with the angle of incidence is related to the elastic properties at the boundary, (see Zoeppritz, K., 1919, "Uber Erbeduellen", Vol. V II, Gottinger Nachrichten, p.66-84). People have paid their attention in recent years to the use of such changes in oil and gas exploration. Wiggins et al put forward a method for determining and displaying the shear-velocity reflectivities, (see Wiggins, R., Kenny, G. S. and McMlure, C. D., 1983, "A method for determining and displaying the shear-velocity reflectivities of a geologic formation", European Patent Application No. 93300227.2). Their formula was derived on the assumption of V.sub.p /V.sub..sigma. =2 which may introduce unpredictable errors to the shear-velocity reflectivity. Because of its insensitivity to pore filling fluids in rocks, the shear-velocity reflectivity can be used in oil and gas explorations, but just because of this insensitivity, its use is limited. The AVO technique utilizes the variation of the P-wave reflection amplitude versus offset to predict the existence of gas reservoir, (see Ostrander, W. J., 1984, "Plane-wave reflection coefficients for gas sands at non-normal angles of incidence", Geophysics, Vol. 49, p. 1637-1648). It has been found that, in many cases, the gradient of P-wave reflection amplitude versus offset from gas-saturated sands encased in shale is bigger than that from brine-saturated sands encased in shale. Both Wiggins's patent and the AVO technique use pre-stacking CDP gathers as input data.
Since the advent of the CDP technique, great efforts have been done to determine compressional velocity V.sub.p and reflection coefficient of P-wave by using P-wave CDP data. Only in recent years did a few researchers suggest methods for determining elastic moduli or their relative changes by using CDP data. Piggott at el presented an iterative approach to determine Poisson ratio .sigma.. Then Piggott at el derived the other four elastic moduli and V.sub..sigma. in terms of .rho. such determined and .rho. and V.sub.p both of which are obtained from other sources, (see Piggott, J. D., Shrestha, R. K and Warwich, R. A., 1989, "Young's modulus from AVO Inversion", 59th Annual International SEG Meeting Expanded Abstracts, p. 832-835). Piggott at el's iterative approach requires that .rho. and V.sub.p are known, which is not realistic. Silva and Ahmed used a simplified approximation to the Zoeppritz equations in which .DELTA..kappa./.kappa. and .DELTA..mu./.kappa. appears as parts of coefficients, (Silva and Aimed's notations are changed to the present invention's for reading consistency). Instead of determining .DELTA..kappa./.kappa. and .DELTA..mu./.kappa., they determined, by fitting the amplitude variation with angle of incidence, the P-wave impedance and a modified version of S-wave impedance. Their approach is, in essence, the same as that of AVO technique, (see Silva, R. and Amhed, H., 1989, "Application of the AVO technique in production geophysics". 59th Annual International SEG Meeting, Expanded Abstracts, p.836-838). Smith and Gidlow presented a "pseudo-Poisson's ratio reflectivity" by subtracting the shear-velocity reflectivity from the compressional-velocity reflectivity, (see Smith, G. C. and Gidlow, P M., 1987, "Weighted stacking for rock property estimation and detection of gas, Geophysical Prospecting", Vol. 35, p.993-1014). It seems that none of the authors mentioned above did a research in earnest in the direction of determining either elastic moduli or their relative changes, but still worked mainly within the scope of conventional physical parameters, not far away from the old track.
The role of the rock's density in oil and gas exploration is well-known. Up till to the present, the conventional method for estimating the density or its relative change from seismic data is as follows: firstly, transforming RMS velocity obtained by velocity analysis into interval velocity (e.g. use Dix's formula), and then using empirical relation (e.g. Gardner's relation) to transform the interval velocity into the density. The density obtained above is of lower reliability, and sometimes is even no use. Extracting density and/or relative chance of the density of geologic formations directly from conventional P-wave seismic data can improve reliability of the density, and can result in a wider scope of its application.
Directly spotting hydrocarbon deposits with conventional P-wave seismic data has been pursued for nearly thirty years. A number of researchers have been working to find a better Direct Hydrocarbon Indicator (hereinafter referred to as DHM). `Blight spot`, `flat point`, `dim zone`, `chimney effect` and `polarity change` were a few of the DHls which achieved only limited success before the advent of AVO technique. AVO technique presents a variety of DHls to explorationists, on which Swan gave an excellent review and discussion (see Swan, H. W., 1993, "Properties of direct AVO hydrocarbon indicators", in Castagna, J. P. and Backus, M. M., Eds., Offset-dependent reflectivity: Theory and practice of AVO analysis: SEG). Castagna and Smith gave a detailed comparison of DHls derived from AVO and presented a new DHl, R.sub.p -Rs with R.sub.p representing P-wave impedance and Rs representing S-wave impedance (see Castagna, J. P. and Smith, S. W., 1994, "Comparison of AVO indicators: A modeling study", Geophysics, Vol. 59, p. 1849-1855). In general, DHls from AVO have better theoretical bases and wider application scope and consequently achieved more success than earlier DHls. However, it has been found that P-wave reflection amplitude from gas-saturated sandstone encased in shale may increase or decrease with angle of incidence, controlled by a set of complicated factors. Moreover, brine-saturated sandstone can also result in amplitude variation versus offset similar to that of gas reservoir. It is difficult in most circumstances to predict hydrocarbon deposits by DHl from AVO. The AVO technique experienced success as well as failure in direct hydrocarbon detection. To find more powerful DHls is still an imminent and significant research task.